I am a student of the Alexander Technique, and while it doesn't address stuttering directly, there are concepts that would apply. I have a slight stutter myself, and have had a couple of students with severe stutters, so I have looked at the application. I will admit that my stutter rarely shows up in teaching or interview situations.
The main tenet of AT that would help is the idea of inhibiting. Not allowing the misuse (or stutter) to happen. The idea is to allow yourself to not speak. Prepare to speak, but if you feel the stutter coming on, allow yourself to not speak - or inhibit the stutter. When you are confident that the act of speaking will be easeful, then speak. In Alexander's own case, it was a tension while orating that was causing him to lose his voice - therefor the idea of preparing to speak with the freedom of not actually having to speak. Obviously this is not something that is an instant fix, and if in an interview you can't just sit there inhibiting, but it is something to explore. In my own case, even before becoming an AT student, if I felt a word sticking, I would pause and find another word. It is sort of the same concept.
A good book to introduce AT is "Body Learning, An Introduction to the Alexander Technique" by Michael Gelb.